# Even Numbers and Odd Numbers

## What is an Even Number

A number that is divisible by 2 and generates a remainder of 0 is called an even number. Examples of even numbers are 2, 4, 6, 8, 10, etc. For example, assume you have ten chocolates. These chocolates may be divided into two groups, each having five chocolates. So, ten is an even number.

## What is an Odd Number

However, 11 chocolates cannot be grouped in this way, so 11 is not an even number. An odd number is a number that is not divisible by 2. The remainder in the case of an odd number is always “1”. 11 is an odd number.

Let’s learn what is an even number:

In the sections below, we’ll look at some additional intriguing methods to grasp even numbers, their features, and fun facts about them.

## How do we identify these numbers?

1. By comprehending the number at the “ones” place

In this approach, we analyze the number in the “ones” place in an integer to check if the number is even or odd. All the numbers ending with 0, 2, 4, 6 and 8 are even numbers. For example, numbers such as 14, 26, 32, 40 and 88 are even numbers.

2. By grouping

If we divide a number into two groups with an equal number of elements in each, then the number is an even number.

## Fascinating Properties of an Even Number

Take a look at the properties of numbers, such as addition, multiplication, and subtraction.

• Adding two even numbers results in an even number. For instance, 12 + 8 = 20.
• An even number plus an odd number equals an odd number. For instance, 6 + 7 = 13.
• When adding two odd numbers, the result is an even number. For instance, 15 + 11 = 26.

### Property of Subtraction

• Subtracting two even numbers results in an even number. For instance, 32 – 6 = 26.
• When you subtract an even from an odd number, the result is an odd number. For instance, 37 – 4 = 33.
• Subtracting two odd numbers results in an even number. For instance, 63 – 17 = 46.

### Property of Multiplication

• When multiplying two even numbers, the result is an even number. For instance, 14 x 2 = 28.
• An even number multiplied by an odd number equals an even number. For instance, 10 x 3 = 30.
• An odd number multiplied by another odd number gives an odd number. For instance, 3 x 5 = 15.

## Solved Examples

Example 1: Is 29510 an even number?

Solution: The ones place of the given number is 0, which is an even number. Thus, the number 29510 is an even number.

Example 2: What is the sum of the first and last even numbers between 1 and 100?

Solution: Between 1 and 100, the largest even number is 98, and the smallest even number is 2.

So, the required sum is 98 + 2 = 100.

Example 3: What is the formula for the sum of the first n even number series?

Solution: The formula of the sum of the first n even numbers is n $\times (n + 1)$.

## Practice Problems

1

### Is 350 an even number?

Yes
No
CorrectIncorrect
350 is an even number because it is exactly divisible by 2.
2

### Which of these are the examples of even numbers?

5, 23, 147
2, 16, 234
89, 573, 1257
123, 567, 897
CorrectIncorrect
Correct answer is: 2, 16, 234
2, 16, 234 are the numbers divisible by 2.
3

### How many even numbers are there between 20 and 50?

13
14
15
16
CorrectIncorrect
There are 16 even numbers between 20 and 50. They are 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50.
4

### What is the sum of all even numbers between 1 and 35?

312
306
364
395
CorrectIncorrect
Formula for sum of even numbers = $S_{n}$ = n(n + 1)
So, $S_{n}$ = n(n + 1) = 17(17+1) = 17*18 = 306